Determine [Zn2 ], [CN–], and [HCN] in a saturated solution of Zn(CN)2 with a fixed pH of 2.780.

Determine [Zn2 ], [CN–], and [HCN] in a saturated solution of Zn(CN)2 with a fixed pH of 2.780. The Ksp for Zn(CN)2 is 3.0 × 10–16. The Ka for HCN is 6.2 × 10–10.

The hint says: Use the systematic treatment of equilibrium to solve this problem. 1. Write the pertinent reactions. 2. Write the charge balance equation. 3. Write the mass balance equations. 4. Write the equilibrium constant expressions for each reaction. 5. Count the equations and unknowns. 6. Solve for all unknowns.

Expert Solution

Zn(CN)2 --->ZN2+ + 2CN-
s 2s

Ksp = [Zn2+] [CN-]^2
3*10^-16 = s * (2s)^2
4s^3= 3*10^-16
s= 4.22*10^-6 M

[Zn2+] = 4.22*10^-6 M
[CN-] = 2s =2* 4.22*10^-6 =8.44*10^-6 M

pH = -log [H+]
2.54= - log [H+]
[H+] = 10^-(2.54)
= 2.88*10^-3 M

Ka= [H+] [ CN-] / [HCN]
6.2*10^-10 = (2.88*10^-3)*(8.44*10^-6) / [HCN]
[HCN] = 39.2 M

queen_honey_blossom answered 2 years ago

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Question

Determine [Zn2 ], [CN–], and [HCN] in a saturated solution of Zn(CN)2 with a fixed pH of 2.780.

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